The invention relates to a method for calibrating a vectorial network analyzer, which exhibits n measurement ports (n>2) and at least m measurement sites, where m>n+1, by means of three different n-port calibration standards, which are connected between the measurement ports in any desired order and which are not permitted to show any transmission, and by successive measurement of the reflection and transmission parameters at different two-port calibration standards, which are connected between the measurement ports in a defined combination and any desired order and must all have a transmission path. By using the measured two-port calibration standards as well as by computational determination of the error-corrected scattering matrices [Sx] of the n-port calibration standards from the error coefficients of each two-port calibration standard, the error coefficients of the network analyzer are computationally determined with the 10-term method in k-fold application, taking into consideration the transmission error variables of the remaining n−2 measurement ports.
Vectorial network analyzers (VNAs) are used for precise measurement of electronic devices and components as well as active and passive high frequency circuits and high frequency modules up to and including antennas.
The customary descriptive model of the electrical behavior of electronic modules and components in high frequency engineering is effected by means of their scattering parameters (also S parameters). They link wave variables with one another, rather than currents and voltages. This representation is particularly adapted to the physical conditions. The so-called scattering parameters of n-ports (n=1, 2, . . . ) are detected and, if necessary, are converted into 2n pole parameters (for example, Z or Y parameters).
The following relationship applies, for example, to the waves a1 and a2, which travel up to a two-port, and the waves b1 and b2, which propagate correspondingly in the opposite direction:
            (                                                  b              1                                                                          b              2                                          )        =                            (                                                                      S                  11                                                                              S                  12                                                                                                      S                  21                                                                              S                  22                                                              )                          ︸                      =                          [              S              ]                                          ⁢              (                                                            a                1                                                                                        a                2                                                    )              ,where [S] is the scattering matrix, which identifies the electronic properties of the two-port.
A so-called system error correction provides for the actual possibility of carrying out precise measurements of the scattering parameters of modules and components using vectorial network analyzers. This system error correction assumes the precise measurement of standards, the electronic behavior of which is known or which can be determined during the system error correction.
It is well known that in the so-called calibration operation, the reflection and/or transmission behavior of calibration standards, which are unknown or partly or completely known, is measured during the system error correction at several measurement sites, which are to be optimized in terms of position and number.
From the measured values of the calibration standards, correction data (so-called error variables or coefficients) are obtained by means of special computation methods. With these correction data and a corresponding correction calculation, measured values, from which system errors of the vectorial network analyzer and of the leads, for example, couplings (cross-talk) or mismatches (reflections) have been eliminated, are obtained for any desired measurement object.
One known calibration method for a two-port model with 10 or 12 error variables is the so-called 10-term or 12-term method. It is also referred to as SOLT (S: Short, O: Open, L: Load=Match, T: Thru) in the American literature and as TMSO in Europe. It is the only system calibration method for two-port network analyzers with just three measurement sites. That is, each measurement site is located at the common measurement channel for both ports before the switch which switches each time one of the ports for measurement, and an additional measurement site at the measurement channel of each port. In this arrangement of the n+1 measurement sites, where n is the number of ports, the switch is integrated in the measurement of the calibration standards.
In the case of this TMSO calibration method, which is used the most often in practice, it is necessary for the two measurement ports to be connected first, which corresponds to the calibration standard T (T=Thru), in order to determine the correction data. Therefore, three one-ports—for example, the calibration standards wave sink (M=Match), short circuit (S=Short) and open circuit (O=Open)—have to be contact-connected and measured at each measurement port. In order to obtain the necessary number of terms for determining the error coefficients from these measurements of the four different calibration standards, it is necessary to know the electronic behavior of all four standards—that is, their transmission and/or reflection behavior. Whereas the calibration standard T exhibits one transmission path (transmission standard) and is realized by means of a direct connection of two measurement ports or one short adapted line, the calibration standards M, S and O do not exhibit any transmission path (reflection standards). The reflection standards are realized by means of impedances—for example, so-called wave terminations with 50Ω (M)—or by means of highly reflecting terminations (O and S).
In modern devices, the measurement accuracy of vectorial network analyzers is influenced almost exclusively by the possibility of realizing the calibration standards required for the system error correction, because the device-internal evaluation of the measurement with the network analyzer assumes that the calibration standards always have ideal values. However, the physically realizable calibration standards are not ideal. It is only possible to realize standards whose electronic properties resemble the ideal standards—for example, open circuit or short circuit. For example, the amount of the reflection factor during a short circuit is always less than one owing to the losses; or the broadband termination shows a significant deviation from the reflection zero especially in the upper frequency range.
The multiport measurement problem lies in the fact that all measurement ports are linked together via the object to be measured. This means that it is no longer the case that a measure of the incident wave is obtained at one measurement site, a measure of the reflected wave is obtained at the next measurement site, and a measure of the transmitted wave is finally obtained at an additional measurement site, independently of the terminations of the multiport. Rather, it is also necessary to take into account the reflection properties of the other measurement ports in the model.
In recent years a number of solutions have been published and patented for this multiport measurement problem. The Ferrero solution to the multiport measurement problem, described by Ferrero, Pisani, Kerwin in “A New Implementation of a Multiport Automatic Network Analyzer”, IEEE Trans. Microwave Theory Techn., vol. 40, November 1992, pp. 2078-2085, requires a network analyzer with 2n measurement sites with the same outlay of calibration standards as the TMSO method. Accordingly, the demands on the hardware of the calibration standards are very complex. Similarly all of the calibration standards have to be completely known in Ferrero's method. This feature is especially disadvantageous since the known standards cannot be perfectly realized. Furthermore, the Ferrero method is based exclusively on the 7-term principle.
As a result there are significant measurement errors, since the known standards have not been perfectly realized and the 7-term principle is sensitive to such model errors, as described by Heuermann in “Sichere Verfahren zur Kalibrierung von Netzwerkanalysatoren für koaxiale und planare Leitungssysteme” [Reliable Methods for Calibrating Network Analyzers for Coaxial and Planar Line Systems], dissertation, Department of High Frequency Engineering, Ruhr University Bochum, 1995, ISBN 3-8265-1495-5.
The DE 199 18 697 A1 describes a 10-term method, which, like the TMSO method, requires just n+1 measurement sites, but only known calibration standards.
Thus, the multiport 7-term methods, which are described in the DE 199 18 960 A1 and are based on an adaptation of the known two-port methods to a multiport method, comprise the TAN, TNA, LAN, TRL, TLR, LLR, LRL, TAR, TMR, TRM, TMS, LMS, TMO, LMO, UMSO, TMN, LNN, TZU, TZY, TYU, LZY, ZZU, YYU, QSOLT methods and usually require n−1+2 calibration measurements.
Another method from the company ATN is described in the U.S. Pat. No. 5,578,932. This patent describes in detail a so-called test set, which can be used to expand a two-port network analyzer to n ports. Furthermore, a special calibration device is described that is required for the automatic calibration of this test set.
This calibration device contains, in addition to the standards open, short and match (also termination), an arrangement of various transmission lines, which can be connected between the terminals of the calibration device via semiconductor switches. Consequently, as in the TMSO method, all of the standards must be completely known. At variance with the statement in the abstract, however, complete multiport calibration and error correction do not occur. Instead, only two-port paths are calibrated; the remaining ports are not taken into account (column 18, line 57).
Two-port measurements are carried out in succession during subsequent measurement operations. In this case the measurement ports, which are not included in the calibration, are terminated one after the other by different reflection standards, which are incorporated within the test set. Precisely one two-port measurement is carried out for each value of the reflection standard (column 21, line 1). Once the measurements have been performed at all of the measurement ports, a result, which has been corrected with respect to the systematic errors, can be calculated from the resulting measured values and the known values of the reflection standards. According to the patent, the measurement of a three-port test object requires two two-port measurements from port 1 to port 2 and from port 1 to port 3 (column 21, line 1 and line 45). In this case, for a complete characterization of all of the parameters, it is necessary to terminate the third port of the test object that was not included in the measurement from port 1 to port 2, by means of at least three different reflection standards (column 21, line 28). This means that the complete characterization of a three-port requires 3+1=4 two-port measurements.
The DE 10 2004 020 037 A1 describes a so-called RRMT calibration method, where, in contrast to the aforementioned methods, not all of the calibration standards have to be known. In a first step the scattering parameters of the unknown calibration standards—Open and Short—are computationally determined from the measurement of the transmission and reflection behavior of the transmission standards, which are known in terms of length and attenuation; the reflection behavior of n known impedances, which are realized at the one-ports, but may be different in comparison to each other, and the n unknown, highly reflecting standards—Open and Short—, in order to determine the error coefficients of the network analyzer with the 10 known terms.
However, the problem in this case is that the measurement of electronic components in the wafer composite (on-wafer measurements) is subject to certain boundary conditions—especially with regard to the possibility of realizing the calibration standards.
In the semiconductor field, it is not unusual for users to realize the calibration standards on the wafers themselves. The geometrical repeatability and uniformity of such self-made calibration standards is very high. In this case it is advantageous that the calibration standards are located on the same substrate carrier (semiconductor) as the measurement objects. In addition to the advantages of short travel distances, it is also possible to “calibrate out” parasitic elements as well as transition effects from the measuring tip to the wafer. However, the electronic properties are realized only to a good approximation. In particular, the reflection standard—Open Circuit—cannot be produced with the necessary quality.
The reflection standards (R) can be described very precisely on semiconductors, but, as a rule, vary widely with regard to the direct current resistance values. In the described methods according to the prior art, it is necessary to connect R standards with the reflection behavior, which is as identical as possible, to each measurement port. If this cannot be ensured, as is the case in multiport on-wafer measurements, since standards have to be routinely arranged at an angle of 90 deg. with respect to one another, then the results are so-called strains that are usually the source of very large measurement errors.
Moreover, the realization of known transmission standards on the wafer is especially problematic. They generally exhibit relatively large deviations from the ideal value. Owing to the arrangement of the ports on the wafer in rows or opposite one another, as shown schematically in FIGS. 1a and 1b with the four ports T1 to T4 and the four transmission standards S1 to S6, and owing to the connection of respectively two of the ports by means of one transmission standard, angles or bends in these standards usually cannot be avoided. For this reason such “bent” transmission standards S3 to S6 always exhibit losses and resonances.
However, such error sources also occur in the production of transmission standards by means of coaxial cables, in so far as, for example, reflecting components, like adapters, are incorporated.